The following has been showed. Consider any sample sequence of a finite length T, ST:={uk|k=1, 2, . . . , T, 0<uk<1} of arbitrary uniform random numbers to be realized on a computer. Then there necessarily exists a multiplicative congruential generator (d, z, n), with its output S:={vk|k=1, 2, . . . , 0<vk<1} with elements approximating those of ST uniformly as |uk−vk|<1/d for any k. This apparently surprising fact stems from all-plain, fundamental structures of our arithmetic of division of an integer n by an integer d with the base z. Yet its implications are fundamental to random number generation problems. First of all, it justifies us to concentrate solely on the design of a multiplicative congruential generator (d, z, n). Second, it erases metaphysical problems, which will arise if we choose the way to doubt whether or not we can generate a random sequence by a deterministic, recursive congruence relations. The simple way out is for us to concentrate only on a solvable technological problem to find a (d, z, n) generator that denies most weakly the statistical hypothesis that the generated sequence S is a sample of uniform and independent random number sequence. The way of thinking gives us great conveniences of spectral tests, which are unambiguous, clear and quantitative way to assess properties (in particular, the independence) of generated random number sequences. It should of course be reminded that, though the said inference ensures any finite portion ST of a uniform random number sequence to admits spectral tests via its approximating multiplicative sequence S, the identification of the modulus d and the multiplier z will generally be highly difficult if we start from ST. The practical possibility of spectral tests is limited to random number sequences generated by multiplicative congruential way to start with. We should further be conscious that the technology never allows us to examine all multiplicative congruential generators. Nevertheless, said clear perspective is encouraging. We may strive along the line of multiplicative congruential way, though only with the setting of a modulus d composed of a prime or two or of their powers adequate for our computing facilities, a multiplier z consisting of primitive roots or of their negatives. The present invention is a report, so to say, that our humble efforts in fact were successful and rewarded by some finite number of excellent generators.